18. Find the product 23cdot 43 modulo 8 A. 3 mod 8 B. 4 mod 8 C. 5 mod 8 D. 6 mod 8

To find the product \(23 \cdot 43\) modulo 8, we first reduce both numbers modulo 8:<br /><br />- \(23 \equiv 3 \pmod{8}\)<br />- \(43 \equiv 3 \pmod{8}\)<br /><br />Next, we multiply the reduced numbers:<br /><br />\[<br />3 \cdot 3 = 9<br />\]<br /><br />Then, we reduce 9 modulo 8:<br /><br />\[<br />9 \equiv 1 \pmod{8}<br />\]<br /><br />Thus, the product \(23 \cdot 43\) modulo 8 is:<br /><br />\[<br />\boxed{1}<br />\]